Discussion
Home ‣ Aptitude ‣ Problems on H.C.F and L.C.M Comments
- Question
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Options- A. 4
- B. 7
- C. 9
- D. 13
- Correct Answer
- 4
Explanation
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)= H.C.F. of 48, 92 and 140 = 4.
- 1. The H.C.F. of 9⁄10, 12⁄25, 18⁄35 and 21⁄40 is:
Options- A. 3⁄5
- B. 252⁄5
- C. 3⁄1400
- D. 63⁄700 Discuss
- 2. Which one of the following numbers is completely divisible by 99?
Options- A. 3572404
- B. 135792
- C. 913464
- D. 114345
- E. None of these Discuss
- 3. 666 / 6 / 3 =?
Options- A. 37
- B. 333
- C. 111
- D. 84
- E. None of these Discuss
- 4. The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800?
Options- A. 16
- B. 24
- C. 20
- D. 18
- E. 22 Discuss
- 5. Which of the following numbers will completely divide (461 + 462 + 463 + 464)?
Options- A. 3
- B. 10
- C. 11
- D. 13 Discuss
- 6. 252 can be expressed as a product of primes as:
Options- A. 2 x 2 x 3 x 3 x 7
- B. 2 x 2 x 2 x 3 x 7
- C. 3 x 3 x 3 x 3 x 7
- D. 2 x 3 x 3 x 3 x 7 Discuss
- 7. The G.C.D. of 1.08, 0.36 and 0.9 is:
Options- A. 0.03
- B. 0.9
- C. 0.18
- D. 0.108 Discuss
- 8. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
Options- A. 9000
- B. 9400
- C. 9600
- D. 9800 Discuss
- 9. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
Options- A. 15 cm
- B. 25 cm
- C. 35 cm
- D. 42 cm Discuss
- 10. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
Options- A. 28
- B. 32
- C. 40
- D. 64 Discuss
Problems on H.C.F and L.C.M
Search Results
Correct Answer: 3⁄1400
Explanation:
| Required H.C.F. = | H.C.F. of 9, 12, 18, 21 | = | 3 |
| L.C.M. of 10, 25, 35, 40 | 1400 |
Correct Answer: 114345
Explanation:
99 = 11 x 9, where 11 and 9 are co-prime.
By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.
Correct Answer: 37
Explanation:
| Given Exp. = 666 x | 1 | x | 1 | = 37 |
| 6 | 3 |
Correct Answer: 24
Explanation:
This is an A.P. in which a = 6, d = 6 and S n = 1800
| Then, | n | [2a + (n - 1)d] = 1800 |
| 2 |
| ⟹ | n | [2 x 6 + (n - 1) x 6] = 1800 |
| 2 |
⟹ 3n (n + 1) = 1800
⟹ n(n + 1) = 600
⟹ n2 + n - 600 = 0
⟹ n2 + 25n - 24n - 600 = 0
⟹ n(n + 25) - 24(n + 25) = 0
⟹ (n + 25)(n - 24) = 0
⟹ n = 24
Number of terms = 24.
Correct Answer: 10
Explanation:
(4 61 + 4 62 + 4 63 + 4 64 ) = 4 61 x (1 + 4 + 4 2 + 4 3 ) = 4 61 x 85
= 460 x (4 x 85)
= (460 x 340), which is divisible by 10.
Correct Answer: 2 x 2 x 3 x 3 x 7
Explanation:
Clearly, 252 = 2 x 2 x 3 x 3 x 7
Correct Answer: 0.18
Explanation:
Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18,
∴ H.C.F. of given numbers = 0.18.
Correct Answer: 9600
Explanation:
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
∴ Required number (9999 - 399) = 9600.
Correct Answer: 35 cm
Explanation:
Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.
Correct Answer: 40
Explanation:
Let the numbers be 2 x and 3 x
Then, their L.C.M. = 6x.
So, 6x = 48 or x = 8.
∴ The numbers are 16 and 24.
Hence, required sum = (16 + 24) = 40.
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